Prime p₀= 1013237793236030561 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 4 2 70 2 58 2 70 2 4 2 (?)
a_n: 0 2 6 8 78 80 138 140 210 212 216 218
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 218
Found by: HenkM
db: batch=76, k=12, 2 4 2 70 2 58

SPT(16)	1013235385951206589	0 12 54 72 78 100 112 124 138 150 162 184 190 208 250 262	-2407284823972
STPT(12)	1013235638725790021	0 2 36 38 48 50 78 80 90 92 126 128	-2154510240540
SPT(16)	1013236724893490051	0 26 42 50 56 78 146 152 276 282 350 372 378 386 402 428	-1068342540510
SPT(16)	1013236814034238601	0 8 42 48 108 126 140 150 188 198 212 230 290 296 330 338	-979201791960
SPT(16)	1013237291508215479	0 40 54 70 144 184 210 228 304 322 348 388 462 478 492 532	-501727815082
STPT(10)	1013237321245305599	0 2 42 44 60 62 78 80 120 122	-471990724962
STPT(10)	1013238222873067067	0 2 30 32 60 62 90 92 120 122	429637036506
SPT(16)	1013238812275913287	0 12 54 102 120 180 240 252 394 406 466 526 544 592 634 646	1019039882726
TPT(14)	1013238924393837299	0 2 12 14 30 32 42 44 72 74 132 134 168 170	1131157806738
STPT(10)	1013239169230220741	0 2 6 8 48 50 90 92 96 98	1375994190180
TPT(14)	1013239310233736819	0 2 60 62 102 104 198 200 210 212 288 290 330 332	1516997706258